"He was fascinated to see the them fly but a little scared when they got a bit close to him," Stillwell tells PEOPLE of the prince's encounter with the Blue Morpho butterfly (known to experts as the Morpho peleides), which is native to Central and South America.

William and Kate – who wore a green silk tea dress by Suzannah – released a statement along with the images to mark their son's birthday.

"We would like to take this opportunity on George's first birthday to thank everyone over the last year, wherever we have met them, both at home and overseas, for their warm and generous good wishes to George and our family," they said.

Stillwell, who has traveled the world covering the royal family, says he kept his distance and used a long lens so William and Kate, both 32, could relax and enjoy the peace at the exhibit with their son.

"As anybody with a young toddler would be, they were very proud parents. They were very relaxed and were happy to be there, showing him around," he says. "They were showing him things, pointing things out. What stands out is how relaxed they are when they are doing something like that. There are no airs and graces."

Sir Michael Dixon, Director of the Natural History Museum, of which Kate is patron, called hosting the family "a real pleasure."

"They seemed to enjoy their visit, wandering through the tropical plants as brightly colored butterflies took flight around them," he added. "It was delightful to see Prince George's first experience of the Natural History Museum and I look forward to welcoming them again in the future."